SOLUTION: Write the equation in slope-intercept form: (2,4) (5,16) Y= use x as a varible Thank you!

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Question 220792: Write the equation in slope-intercept form:
(2,4) (5,16)
Y=
use x as a varible
Thank you!
Found 2 solutions by rfer, jim_thompson5910:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
y=mx+b
y=4x-4

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=5 and y%5B2%5D=16.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2816-4%29%2F%285-2%29 Plug in y%5B2%5D=16, y%5B1%5D=4, x%5B2%5D=5, and x%5B1%5D=2


m=%2812%29%2F%285-2%29 Subtract 4 from 16 to get 12


m=%2812%29%2F%283%29 Subtract 2 from 5 to get 3


m=4 Reduce


So the slope of the line that goes through the points and is m=4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-4=4%28x-2%29 Plug in m=4, x%5B1%5D=2, and y%5B1%5D=4


y-4=4x%2B4%28-2%29 Distribute


y-4=4x-8 Multiply


y=4x-8%2B4 Add 4 to both sides.


y=4x-4 Combine like terms.


So the equation that goes through the points and is y=4x-4


Notice how the graph of y=4x-4 goes through the points and . So this visually verifies our answer.
Graph of y=4x-4 through the points and